Extreme value theory and value-at-risk : empirical evidence from the London Metal Exchange
Κατσιαβριάς, Δημήτριος Γ.
It compares the predictive ability of eight Value-at-Risk methods includingGARCH(1,1) with Normal and t-Student innovations, Exponential GARCH(1,1) with Normal and t-Student innovations, Exponentially Weighted Moving Average (EWMA), Historical Simulation, Block Maxima (GEV Distribution) and Peaks over Threshold (GP Distribution) for the period 1/6/1989-2/3/2007 on cash and 3-month futures logarithmic price changes of Copper, Tin, Zinc, Nickel and Aluminium, metals that trade in the London Metal Exchange. It also analyzed equity market data (FTSE-100 & LIFFE FTSE-100) and Gold Bullion data for the same period, in order to compare the industrial metals market with equity and precious metals. The metals of the London Metal Exchange proved riskier than equity and gold, with Nickel being the riskier of all in terms of mean VaR. Its findings support the models that assume time-varying volatility as they proved very important in predicting the Value-at-Risk measure, especially the GARCH and EGARCH with t-Student distributed innovations. Block Maxima performed badly whereas Peaks over Threshold showed some forecasting ability especially in the Nickel time series. Moreover, Stress Testing proved that conditional volatility models and especially the t-Student GARCH(1,1) and EGARCH(1,1) can predict large negative returns. Extreme Value Theory is an important tool in Risk Management but one should be cautious as the methods of EVT need large data sets for the estimation process and moreover different assumptions about the block size and the number of blocks for Block Maxima and the determination of the threshold u for Peaks over Threshold may lead to different than expected results.